The simple algebraic transformations using the approximation of transfer function by K( s) =[sigma]p kp exp( -stp) or the approximation of convolution by: [formula] enable the creation of models of dynamics in the form of first-order (linear) differential equations with deviated arguments. The suita[...]

In the paper, the solution of second order differential equations with various coefficients is presented. The concerning equations are written as first order matrix differential equations and solved with the use of the power series method. Examples of application of the proposed method to the equati[...]

The sufficient conditions of asymptotic string stability in large of some finite composite stochastic systems are established. Nonlinear systems are considered with random noise which obeys the law of large numbers. The objective is to analyze composite systems in their lower order subsystems and in[...]

The paper deals with the initial boundary value problem for quasilinear first order partial differential functional equations. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional equations are present[...]

Tabular functions were invented to form a formal framework for normal and inverted function tables used in documenting complex software systems. They are defined as maps on finite partitions of a given nonempty set X with values in a set of function symbols. It is shown that every tabular function i[...]

In this paper stability in the Kozin sense and boundness of the solutions of some evolution equations with non-linearity is investigated. The conditions for boundness and Kozin stability of solutions were obtained.

Correctness of some inequalities concerning solution of the equation the abstract differential equations is proved with adequate conditions as is stability of the equation's solutions in the Kozin's sense.

In the article we consider the two-dimensional heat equation in a circular domain where the thermal diffusivity is a piecewise constant function in the radial directon and is a constant function in the angular direction. In particular we consider the problem of computation of a perturbation in this [...]

The paper investigates the existence and uniqueness of the weak solution to the initial boundary value problem for a system consisting of a hyperbolic-type partial differential equation with distributional coefficients and a collection of ordinary differential equations, modelling small vibrations o[...]

In this paper the problem of solution of ordinary differential equations describing a steady, gradually varied flow is discussed. It is shown that, apart from the initial problem usually solved for open channels, the formulation of the boundary problem is necessary when water levels are imposed at e[...]

The Laplace transform is powerful method for solving differential equations.
This paper presents the application of Laplace transform to solve the
mathematical model of gas flow through the measuring system. The basis of the
mathematical model used to describe and simulate the analyzed process is a
[...]

The work concerns training neural networks for approximate mappings being solutions to differential equations, especially partial-differential equations. The presented approaches falI into two categories. In the first one, backpropagation training is combined with an arbitrary numerical method used [...]

The paper presents the theorems about regularity of systems of differential equations. The paper is divided into two parts. The first part contains a theoretical introduction. The second part contains theorems which allows to determine the regularity of the system using the generalized Lyapunov func[...]

The paper considers the problem of practical using of theory about near-critical flows. It describes the types of immovable and movable near-critical flow phenomena and cases of these phenomena formation during different hydrotechnical constructions operating. The paper gives generalized differentia[...]

The foundations of the vector analysis in the Bittner Operational Calculus are elaborated in the paper. Particularly the Poincare Lemma and Helmholtz Theorem are formulated and proved. Both of them are the generalizations of the classical theorems of the vector analysis in R .